COUPLING VIBRATION OF VEHICLE-BRIDGE SYSTEM

By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system was developed. The model was solved by mode analyzing method and Runge-Kutta method, and the dynamic response and the resonance curve of the bridge were obtained. It is found that there are two resonance regions, one represents the main resonance while the other the minor resonance, in the resonance curve. The influence due to the rugged surface, the vibration mode of bridge, and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effect of roughness of the bridge deck and the mode shape of the bridge can't be ignored and the vehicle velocity should be kept away from the critical speed of the vehicle.

Numerical analysis of dynamic response of vehicle–bridge coupled system on long-span continuous girder bridge

To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.

Natural Frequency of the Bridge—Vehicle Coupled System Considering Uniform Distributed Moving Load

Natural frequencies of the bridge—vehicle coupling system considering uniform distributed load varying with position is investigated in this work.An analytic model of a simply supported beam bridge with constant section is introduced to establish the frequency equations of the coupled system.Comparisons with the results between analytic model and FEM indicate that the present research is correct and reasonable.In view of an example bridge,natural frequencies are studied on the bridge subjected to uniform distributed moving loads in cases of different weight and span,by which some regular phenomenon are obtained.The present study can apply in the engineering problem of interaction between bridges and moving loads such as trains and tracked vehicles.

A vertical coupling dynamic analysis method and engineering application of vehicle–track–substructure based on forced vibration

Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h
1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

Impact coefficient and reliability of mid-span continuous beam bridge under action of extra heavy vehicle with low speed

To analyze the dynamic response and reliability of a continuous beam bridge under the action of an extra heavy vehicle, a vehicle–bridge coupled vibration model was established based on the virtual work principle and vehicle–bridge displacement compatibility equation, which can accurately simulate the dynamic characteristics of the vehicle and bridge. Results show that deck roughness has an important function in the effect of the vehicle on the bridge. When an extra heavy vehicle passes through the continuous beam bridge at a low speed of 5 km/h, the impact coefficient reaches a high value, which should not be disregarded in bridge safety assessments. Considering that no specific law exists between the impact coefficient and vehicle speed, vehicle speed should not be unduly limited and deck roughness repairing should be paid considerable attention. Deck roughness has a significant influence on the reliability index, which decreases as deck roughness increases. For the continuous beam bridge in this work, the reliability index of each control section is greater than the minimum reliability index. No reinforcement measures are required for over-sized transport.

Seismic response analysis of road vehicle-bridge system for continuous rigid frame bridges with high piers

The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the extemal excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.

Dynamic Characteristics of Metro Vehicle under Thermal Deformation of Long-Span Cable-Stayed Bridge

In order to study the influence of thermal deformation of long-span cable- stayed bridge (LSCSB) on the dynamic characteristics of metro vehicle on the bridge, based on the theory of vehicle-track coupled dynamics, the rigid-flexible coupled dynamic model of metro vehicle-track-LSCSB system is established by using finite element method and multi-rigid-body dynamics. Adopting this model, the deformation of LSCSB subject to temperature is analyzed, then the comprehensive effect of track random irregularity and rail deformation caused by temperature load is considered to study the dynamic characteristics of metro vehicle running through the bridge, and finally the influences of temperature increment and running speed on concerned dynamic indices of vehicle are studied. The results show that the LSCSB deforms obviously subject to temperature load, and the overall performance is that the cooling is arched, and the heating is bent, and the shape variable changes almost linearly with the temperature load. According to the parameters studied in this paper, the rail deformation caused by temperature load increases the wheel-rail vertical force, derailment coefficient and wheel load reduction rate by 1.5%, 3.1% and 5% respectively. The vertical acceleration of the vehicle body decreases by 2.4% under the cooling condition, while increases by 3.7% under the heating condition. The dynamic response of the bridge changes under temperature load. The maximum vertical and horizontal displacement in the middle of the main beam span are 6.24 mm and 2.19 mm respectively, and the maximum vertical and horizontal acceleration are 1.29 cm/s2 and 2.54cm/s2 respectively. The derailment coefficient and vertical acceleration of vehicle body are more affected by temperature load, and the wheel load reduction rate and wheel-rail vertical force are more affected by speed. The conclusion of this paper provides a reference for subsequent scholars to study the influence of thermal deformation on the dynamic response of vehicles on LSCSB.

Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Employing theory on vehicle-track coupled dynamics, the equation of motion of a vehicle-track vertical coupled system was established by combining frequency analysis and symplectic mathematics. The frequency response of the vehicle-track vertical coupled system was calculated under the excitation of the German low-interfer- ence spectrum, and the effects of the vehicle speed, vehicle suspension parameters, and track support parameters on the frequency response of the coupled system were studied. Results show that, under the excitation of the German low- interference spectrum, the vertical vibration of the car body is mainly concentrated in the low-frequency band, while that of the bogie has a wide frequency distribution, being strong from several Hertz to dozens of Hertz. The vertical vibrations of the wheel-rail force, wheelset, and track structure mainly occur at a frequency of dozens of Hertz. In general, the vertical vibration of the vehicle-track coupled system increases with vehicle speed, and the vertical vibrations of the car body and bogie obviously shift to higher frequency. Increasing the vehicle suspension stiffness increases the low- frequency vibrations of the vehicle system and track struc- ture. With an increase in vehicle suspension damping, the low-frequency vibrations of the car body and bogie and the vibrations of the wheel-rail vertical force and track structure decrease at 50-80 Hz, while the mid-frequency and high- frequency vibrations of the car body and bogie increase. Similarly, an increase in track stiffness amplifies the vertical vibrations of the wheel-rail force and track structure, while an increase in track damping effectively reduces the vertical vibrations of the wheel-rail vertical force and track structure.

Turning traction force of tracked mining vehicle based on rheological property of deep-sea sediment

Based on main physical and mechanical properties of deep-sea sediment from C-C poly-metallic nodule mining area in the Pacific Ocean, the best sediment simulant was successfully prepared by mixing bentonite with a certain content of water. Compression-shear coupling rheological constitutive model of the sediment simulant was established by endochronic theory and the coupling rheological parameters were obtained by compressive and compression-shear creep tests. A new calculation formula of turning traction force of the tracked mining vehicle was first derived based on the coupling rheological model and consideration of pushing resistance and sinkage of the tracked mining vehicle. Effects of the turning velocity, crawler spacing and contacting length of crawler with deep-sea sediment on the turning traction force were analyzed. Research results can provide theoretical foundation for operation safety and optimal design of the tracked mining vehicle.

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor （LIM） vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen– Hedrick–Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system （LMS）, Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.

Dynamic Response of Elastic Sleeper Ballasted Track on Bridge

A vehicle-track-bridge coupling dynamics model was built based on the theory of vehicle-track coupling dynamics. Using this model, a comparison was made between the dynamic response of an elastic sleeper ballasted track and a common sleeper ballasted track on bridge under the same working conditions. The results show that laying elastic sleepers on the bridge could solve the problem of large track stiffness caused by a thin ballast thickness, and improve the dynamic response of the bridge. This is beneficial to train operation safety and riding comfort.

Occasional Forces and Displacements of Longitudinally Coupled Ballastless Jointless Turnout on Bridges

For the longitudinally coupled baUastless turnout on Leida bridge on Wuhan-Guangzhou passenger dedicated line （PDL） in China, a turnout （cross over）-track slab-bridge deck-pier integrated finite element model was established, in which two No. 18 jointless turnouts with movable frogs in form of crossover, longitudinally coupled ballastless track, bridges and piers were regarded as one system. Based on this model, the additional forces and displacement regularities of turnouts, track slab, bridges and piers under occasional loading were analyzed, and the effect of occasional loading position was researched. The results show that slab breaking is more influential on the longitudinal force and deformation of the whole system than rail breaking, that slab breaking on one line could deteriorate both the slab force on another line and the forces exerted on the piers and fastener components, and that a great slab force at the left end of the continuous bridge expansion joint should be particularly avoided in design.

AN INTEGRATED COUPLING ELEMENT FOR VEHICLE-RAIL-BRIDGE INTERACTION SYSTEM WITH A NON-UNIFORM CONTINUOUS BRIDGE

An integrated coupling element considering wheel-rail interface for analyzing the dynamic responses of vehicle-rail-bridge interaction system with a non-uniform continuous bridge is presented. The governing equations of the interaction system are established first, and the solution procedure and assembly method of the coupling element are demonstrated. Finally, the accuracy, efficiency and function of the integrated coupling element are tested using two numerical examples. The influences of different combinations of rail and bridge element length in the coupling element on the solution are investigated, and the effects of different rail irregularities on the dynamic responses are discussed.

高速铁路主跨320 m钢-混部分斜拉桥无砟轨道适应性研究

南玉高铁六景郁江特大桥设计将钢-混部分斜拉桥结构引入时速350 km高速铁路领域,而300 m级以上大跨度桥上无砟轨道的竖向变形极易超限,影响列车通过的安全性和舒适性,因此,系统研究在此大跨桥梁结构上铺设无砟轨道的适应性十分必要。通过建立有限元及动力学模型,分析不同组合工况下无砟轨道结构的变形特点及动力特性,运用60 m弦测法探究各工况下无砟轨道的线形变化规律,从而确定大跨度钢-混部分斜拉桥铺设无砟轨道的适应性,并对设计和施工提出合理化建议。主要结论如下:在各种不利组合荷载作用下,桥上无砟轨道结构强度满足规范要求,列车通过大桥的各项安全性与舒适性指标均满足规范要求;混凝土收缩徐变和斜拉索升降温是影响无砟轨道线形标准的两大主因,应在无砟轨道施工前确保足够的沉降观测期和收缩徐变释放期,并充分考虑拉索的保温设计;在温度组合荷载作用下,桥上无砟轨道的60 m弦测不平顺幅值为6.79 mm,满足高速铁路静态验收标准;但在叠加列车荷载和收缩徐变后,变形弦测值均出现Ⅱ级及以上超限,通过合理设置预拱度后可有效改善轨道平顺性标准。

9号道岔区铺设减振垫浮置板的行车安全性及舒适性研究

地铁道岔区在基本轨、尖轨处以及道岔钢轨接头处存在大量钢轨不连续地段,轮轨相互作用强烈,轨道系统振动明显,减振垫浮置板轨道作为一种高等减振措施已应用于地铁线路道岔区。为探究减振垫浮置板应用于9号道岔的适用性,并作为减振地段与普通无砟轨道的过渡段的可行性,以某地铁高架9号道岔为研究对象,建立桥上道岔三维有限元模型,仿真分析地铁B型车在120 km/h直向过岔和30 km/h侧向过岔的情况下,列车的行车安全性、舒适性以及轨下结构形变。对比在9号单开道岔区域设置的2种刚度过渡方式的优劣及其减振效果,较为系统地论证了在9号道岔区域铺设减振垫浮置板的可行性。研究结果表明:1)列车通过铺设减振垫浮置板的9号道岔区域时,浮置板位移极值出现在转辙区域和心轨区域,最大位移出现在尖轨位置,可增大尖轨处单板橡胶垫支承刚度,以保证轨道结构变形均匀;2)列车逆向侧向通过设置过渡段的减振垫浮置板道岔区时,2级过渡方式的车体最大垂向加速度、最大横向加速度、最大脱轨系数、最大轮重减载率、轨道刚度变化率以及减振效果等指标均优于1级过渡方式;3)在道岔区铺设减振垫浮置板,列车直向和侧向通过时的行车安全性和舒适性均能满足相关评价指标,且2级过渡方式更优。研究结果可为后续道岔区减振设计研究提供一定的理论参考。

考虑加载历史的小半径曲线桥梁梁轨相互作用分析

目前,大部分考虑加载历史的梁轨相互作用研究都集中在直线桥梁上,针对曲线桥梁,尤其是小半径曲线桥梁,梁轨相互作用的研究相对较少。采用理想弹塑性滞回阻力模型模拟扣件纵向阻力,运用有限元软件,建立以城东特大桥为研究对象的钢轨-桥梁-墩台三维有限元空间力学计算模型,研究曲线半径对于梁轨相互作用的影响,探究了多荷载耦合作用、往复荷载作用以及循环荷载作用下考虑加载历史效应的曲线桥梁梁轨相互作用情况,并提出“拉力百分比”以及“压力百分比”的概念以便分析曲线半径对传统线性叠加法误差的影响。结果表明,曲线桥梁中梁轨纵、横向相互作用分别与曲线半径成正、反比,相关数据改变幅度与曲线半径成反比且当曲线半径超过800 m时基本收敛,此时可采用“以直代曲”的简化算法;曲线半径对于横向梁轨相互作用影响程度大于纵向,相较于挠曲、制动工况,伸缩工况受曲线半径影响更加显著;多荷载耦合作用下,采用传统线性叠加法相较于考虑加载历史更为保守且温度荷载起主要贡献;考虑加载历史时钢轨在往复荷载作用下会产生不可忽视的残余内力,且在循环荷载作用下将会产生收敛于第1次往复荷载下的残余内力,这是扣件纵向阻力的弹塑性滞回特性决定的;线性叠加法误差与曲线半径具有相关性,相较于挠曲、制动工况,伸缩工况下对其更为敏感。研究结果可为考虑加载历史下曲线桥梁结构设计提供参考。

波浪荷载作用下车辆-轨道-悬浮隧道动力响应研究

为实现波浪荷载作用下车辆-轨道-悬浮隧道系统耦合动力学行为模拟和分析,基于车辆-轨道耦合动力学理论,引入轮轨非线性时变单元矩阵法和结构单元多尺度耦合法,采用弹簧-阻尼单元模拟锚索系统,建立车辆-轨道-悬浮隧道动力相互作用模型;根据线性波浪理论和Morison方程,确定波浪荷载计算方法;最后,基于所建立的车辆-轨道-悬浮隧道动力相互作用模型开展数值仿真模拟,研究波浪荷载作用下锚索等效刚度、波浪高度、行车速度等参数变化时系统振动响应特性及传播规律。研究结果表明:锚索等效刚度变化对轨道-悬浮隧道系统结构位移的影响显著,提高锚索等效刚度能够有效抑制结构位移增大,且考虑部分锚索失效后系统结构位移变化较大,位移增幅均大于43%,不利于结构稳定;轨道-悬浮隧道系统结构的横向位移主要由波浪荷载引起,随着波浪高度增加,轨道-悬浮隧道系统结构位移整体上呈增大趋势;在工程设计过程中,应充分调研场地水环境,并合理设置轨道-悬浮隧道系统的结构参数,以确保系统的安全性和稳定性。

抢险车对92m跨度复合材料桁架桥动态响应的影响

为研究大跨径桁架式纤维增强复合材料(FRP)应急抢修桥梁成桥后的动力性能,基于导梁推送施工92 m跨度的FRP桁架桥模型,编制FRP桁架桥的车桥耦合算法,研究抢险车辆的车速、质量及路面不平顺对FRP桁架桥的跨中竖向位移、竖向加速度和关键杆件轴向应力等指标的影响.结果表明:路面越不平顺,车辆对桥梁结构的冲击作用越大,且路面等级对竖向位移的影响大于对关键杆件轴向应力的影响;车速为20~50 km/h时,车速变化对冲击系数影响较小,但车速超过50 km/h时,车速的影响逐渐增大;车辆质量对桥梁各项指标动力响应的峰值曲线呈线性增大趋势.当车辆质量为2.80×10^(4)kg,车速30 km/h时,最大跨中竖向位移为167 mm,未超过抢修桥梁位移限值(L/120),表明该桥梁的设计可以满足抢险的通行要求.

基于交叉迭代法的车辆-轨道非线性空间耦合振动模型及算法改进

针对车辆-轨道非线性空间耦合系统动力学分析计算量大、计算耗时长及计算精度难以保证的问题,对车辆-轨道非线性空间耦合振动模型和交叉迭代法进行改进。运用有限元法分别建立车辆和轨道空间子系统动力学模型,在基于“迹线法”构建轮轨接触几何关系的基础上,提出“投影对点作差法”搜索轮轨空间接触点位置,并引入轮轨准弹性接触对其进行修正,精细化轮轨接触关系;结合车辆-轨道非线性空间耦合系统特点,改进基于Newmark数值积分的交叉迭代求解系统动力学方程的算法,并给出完整的数值计算步骤。通过与相关文献进行对比,验证改进模型和算法的有效性。结果表明:改进模型的分析精度更高,搜索轮轨空间接触点位置的速度更快;改进算法的计算过程更完善,步骤更清晰;改进的模型和算法在提高计算精度的同时,仍然具有较快的计算效率,且使数值编程更易实现,方便工程应用。

基于等效刚度阻尼系统的中低速磁浮列车与大跨度桥梁耦合振动响应分析

针对中低速磁浮列车与大跨度连续梁桥的耦合动力响应问题,本文基于等效刚度阻尼系统建立多编组磁浮列车模型;基于国内在建磁浮专线连续梁桥(35m+55m+35m),采用ANSYS中实体单元建立全桥模型.并将两个独立系统在SIMPACK进行车桥耦合,设定车重参数分别为空载、定员和超载,且列车按单线和双线工况运行,计算耦合系统的动力响应.结果表明,本文建立的列车模型受到轨道激励时,磁浮间隙在额定范围内浮动,即等效刚度阻尼系统有良好的控制效果;车辆磁浮间隙的变化量、车体竖向加速度与车重成反比,而磁浮力与车重成正比;在计算工况下,桥梁主跨及边跨的竖向位移均满足设计要求的限值,双线列车超载运行桥梁跨中最大位移仅为4.503mm.说明连续梁桥具有较大的刚度,能满足磁浮车辆安全运行的要求;对比列车单双线运行,主跨跨中的竖向位移最大值后者达到前者两倍,而边跨位移的最大值后者仅比前者增大70%,表明双线列车对开运行对桥梁的动力响应存在增大效应.相关研究成果对磁浮线路建设有一定参考意义.